Chapter 9—Ideal Gas Law. Today we move into Chapter 5, quite possibly the easiest chapter (in terms of problems) this term. Can you remember one simple equation? If so, then Chapter 9 will be ridiculously simple PV = nRT Five types of problems come from that equation
1 atm = 760 mmHg
= 760 Torr
= 101.325 kPa
PV = constant or PinitialVinitial = PfinalVfinal
Van V = cn V/n = c
What is the pressure exerted by 0.508 mol O2 in a 15.0-L container at 303 K?
P = nRT/V (0.508 mol)(0.08206 L atm/mol K)(303) / 15 L
don’t screw up data entry into the calculator…
What is the volume occupied by 16.0 g ethane gas (C2H6) at 720 Torr and 18 °C?
ooooo!!! A wrinkle—conversions!
g—mol, Torr—atm and C—K, plug/chug and done
—— = constant
We can cancel any term (P, V, n, T) that is the same on both sides.
—— = ——
—— = ——
The flasks pictured in the cartoon below contain O2(g), the one on the left at STP and the one on the right at 100 °C. What is the pressure at 100 °C?
SAME # moles, SAME volume…
What pressure would be exerted if the vessel were transferred to an oil bath at 200 °C?
M = molar mass and m = mass in grams
m (grams) m
M =————— so n = —
n (moles) M
The ideal gas equation rearranges to:
Setting the equations equal to one another:
Alternative to equation: (A) find n using the ideal gas equation; (B) Divide m (grams) by n (moles) to get grams/mol.
… and solving for M:
If 0.550 g of a gas occupies 0.200 L at 0.968 atm and 289 K, what is the molecular mass of the gas?
Calculate the molecular mass of a liquid that, when vaporized at 100 °C and 755 Torr, yields 185 mL of vapor that has a mass of 0.523 g.
Density of a gas is directly proportional to its molar mass and pressure, and is inversely proportional to Kelvin temperature.
Alternative: find volume of one mole (n = 1) or other fixed quantity of gas. Divide mass of that quantity by volume to find g/L.
mRT m MP
M =——— rearranges to — = ——
PV V RT
and density = — so d = ——
Calculate the density of methane gas, CH what is the molecular mass of the gas?4, in grams per liter at 25 °C and 0.978 atm.
Under what pressure must O2(g) be maintained at 25 °C to have a density of 1.50 g/L?